Practical Inner Codes for BATS Codes in Multi-Hop Wireless Networks

Batched sparse (BATS) codes are a promising technique for reliable data transmission in multihop wireless networks. A BATS code consists of an outer code and an inner code, the design of which can be separated. In this paper, we investigate the design of the inner code and focus on maximizing the expected batch transfer matrix rank normalized by the total number of packets transmitted by both the source and intermediate nodes. By allowing different recoding decisions at different nodes, the problem is formulated as a nonlinear integer programming (NLIP) problem, which is non-deterministic polynomial (NP)-hard in general. We derive a noniterative formula to simplify the evaluation of the expected batch transfer matrix rank. By considering large finite fields and relaxing the integer constraints, we obtain an upper bound on the optimal value of the original maximization NLIP problem. We also derive a centralized and a decentralized algorithm to find suboptimal solutions of the NLIP problem, with different tradeoffs between complexity and performance. Numerical results show that our proposed inner codes outperform the standard BATS, and achieve very close to the upper bound, which verifies the near optimality of our algorithms.